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07exLRs1a

# 07exLRs1a - ISOM111 Business Statistics(Fall 2010 Suggested...

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ISOM111 Business Statistics (Fall 2010) Suggested Solutions for Tutorial Set 7 Exercise (Q1 Part a) 1. (a) The dependent variable is the number of homes sold annually & the independent variable is the annual mortgage rate. (b) x = 9 . 62 s X = 1.3448 P x 2 = 941 . 72 y = 349 . 1 s Y = 25.1106 P y 2 = 1224383 P xy = 33388 . 1 n = 10 SSX = P x 2 n x 2 = P x 2 ( P x ) 2 n = ( n 1) s 2 X = 16 . 276 SSY = P y 2 n y 2 = P y 2 ( P y ) 2 n = ( n 1) s 2 Y = 5674 . 9 SSXY = P xy n x y = P xy P x P y n = 195 . 32 b β 1 = SSXY SSX = 195 . 32 16 . 276 = 12 . 000 b β 0 = y b β 1 x = 349 . 1 ( 12 . 000)(9 . 62) = 464 . 54 b Y = 464 . 54 12 . 000 X (c) If the annual mortgage rate is 0%, the average number of homes sold is expected to be 464540 . It is not meaningful to interpret the Y intercept because the mortgage interest rate cannot be equal to 0% in practice. 464540 is the portion of number of homes sold annually that varies with factors other than the mortgage interest rate. (d) s = s SSE n 2 where SSE = SSY ( SSXY ) 2 SSX = 5674 . 9 ( 195 . 32) 2 16 . 276 = 3330 . 964 s = 20 . 4052 (e) r = SSXY SSX SSY = 0 . 6427 1

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(f) H 0 : β 1 = 0 vs H a : β 1 6 = 0 With α = 0 . 1 ,
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07exLRs1a - ISOM111 Business Statistics(Fall 2010 Suggested...

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